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One part of a hostel’s monthly expenses is fixed, and the other part is proportional to the number of its boarders. The hostel collects $₹ \; 1600$ per month from each boarder. When the number of boarders is $50,$ the profit of the hostel is $₹ \; 200$ per boarder, and when the number of boarders is $75,$ the profit of the hostel is $₹ \; 250$ per boarder. When the number of boarders is $80,$ the total profit of the hostel, in $\text{INR},$ will be

1. $20800$
2. $20200$
3. $20000$
4. $20500$

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